摘要
Consider the Cauchy problem of a time-periodic Hamilton-Jacobi equation on a closed manifold,where the Hamiltonian satisfies the condition:The Aubry set of the corresponding Hamiltonian system consists of one hyperbolic 1-periodic orbit.It is proved that the unique viscosity solution of Cauchy problem converges exponentially fast to a1-periodic viscosity solution of the Hamilton-Jacobi equation as the time tends to infinity.
Consider the Cauchy problem of a time-periodic Hamilton-Jacobi equation on a closed manifold, where the Hamiltonian satisfies the condition： The Aubry set of the corresponding Hamiltonian system consists of one hyperbolic 1-periodic orbit. It is proved that the unique viscosity solution of Cauchy problem converges exponentially fast to a 1-periodic viscosity solution of the Hamilton-Jacobi equation as the time tends to infinity.
基金
supported by the National Natural Science Foundation of China(No.11371167)
